A215417 Primes that remain prime when a single zero digit is inserted between any two adjacent digits.

11, 13, 17, 19, 37, 41, 53, 59, 61, 67, 71, 79, 89, 97, 109, 113, 131, 149, 191, 197, 227, 239, 269, 281, 283, 337, 367, 379, 383, 401, 421, 449, 457, 499, 503, 509, 587, 607, 673, 701, 719, 727, 739, 757, 809, 811, 887, 907, 929, 991, 1009, 1061, 1093, 1103

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..4300 (terms a(1)-a(372) from Paolo P. Lava, terms a(373)-a(700) from Vincenzo Librandi)

Example

399617 is prime and also 3996107, 3996017, 3990617, 3909617, 3099617.

Maple

A215417:=proc(q)
local a, b, c, i, n, ok;
for n from 5 to q do
  a:=ithprime(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od;
  a:=ithprime(n); ok:=1;
  for i from 1 to b-1 do
    c:=a+9*10^i*trunc(a/10^i); if not isprime(c) then ok:=0; break; fi;
  od;
  if ok=1 then print(ithprime(n)); fi;
od; end:
A215417(1000);

Mathematica

Select[Prime[Range[5, 200]], And@@PrimeQ[Table[FromDigits[Insert[ IntegerDigits[ #], 0, n]], {n, 2, IntegerLength[#]}]]&] (* Harvey P. Dale, Feb 23 2014 *)

Prog

(PARI) is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=0; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Cf. A159236, A069246, A215419-A215421.

Sequence in context: A050674 A164329 A159236 * A249376 A068155 A271367

Adjacent sequences: A215414 A215415 A215416 * A215418 A215419 A215420

Keyword

nonn,base

Author

Paolo P. Lava, Aug 10 2012

Status

approved